Connections Between f, f', and f"

If f '(x) is given, which could be f(x)?

• A

• B

• C

If a function has a derivative that is positive, what does that tell you?

• The function is increasing

• The function is has a y-value that is positive

• The function is concave up

• More information is needed

For some function f that is differentiable on its entire domain, what must occur at every stationary point?

• f '(c) = 0

• f '(c) is undefined

• f(c) = 0

• None of the above

The graph of f ', the derivative of f, is shown for -2 ≤ x ≤ 5. On what intervals is f increasing?

• (-2,3)

• (-2,1) ∪ (1,2)

• (3,5)

• (-1,1) ∪ (2,3)

The graph of f(x) is shown. Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)

• (-3, 1)

• (-5, 0) ∪ (2, ∞)

• (-5, ∞)

At what x-value(s) does f(x) have a minimum?

• x = -3
• x = 1
• x = 5
• x = -3 and x = 5

If a function's first derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point

• The function is decreasing at that point

• The concavity of the function is up at that point

• The concavity of the function is down at that point

Given a function g(x) at some point c, if g'(c)=0 and g"(c)>0, then g(x) has _______________ at c.

• an inflection point

• an x-intercept

• a minimum

• a maximum

For a function g(x), g'(-2)=3 indicates g(x) is ________________ at x = -2.

• decreasing

• increasing

• concave up

• concave down

For a function f(x), f"(-3) = 5 indicates f(x) is _______________ at x = -3.

• increasing

• decreasing

• concave up

• concave down